Question

Calculate the Laplace transforms of the following from the definition. 1. y = t^2. y = t^3

Answer 1

1)
`L(y)=(2)/(s^(3))`

2)
`L(y)=(6)/(s^(4))`

Explanation:

To find : Calculate the Laplace transforms of the following from the definition ?

Solution :

We know that,

Laplace transforms of
`t^n` is given by,

`L(t^n)=(n!)/(s^(n+1))`

1)
`y=t^2`

Laplace of y,

`L(y)=L(t^2)` here n=2

`L(y)=(2!)/(s^(2+1))`

`L(y)=(2)/(s^(3))`

2)
`y=t^3`

Laplace of y,

`L(y)=L(t^3)` here n=3

`L(y)=(3!)/(s^(3+1))`

`L(y)=(3* 2)/(s^(4))`

`L(y)=(6)/(s^(4))`